Modeling of bouncing of a single clean bubble on a free surface

Bouncing of a rectilinearly rising bubble on a free surface is modeled with the use of a simple mass-spring system. The most striking characteristic of the present model is that it is based on an equation of motion of the system that consists of two springs connected in series; hence, we can account for the restoring forces of both the bubble and free surfaces. This equation of motion is coupled with a conservation equation of energy that is taking into account an exchange between the surface energy due to deformations of both the bubble and free surfaces and the kinetic energy of the bubble. With the use of these equations, the contact time, i.e., the time duration of a bubble contacting a free surface, is determined to be a half of the characteristic period of the oscillator. We also conducted experiments of a single clean bubble in ultrapure water bouncing on a flat free surface in order to verify the present model. We found that results obtained from the model agree well with the experimentally obtained results, even in cases with significant surface deformations. When bubbles are smaller than 0.6 mm in radius, the deformations of both the bubble and free surfaces play important roles in bouncing. In case of larger bubbles, on the other hand, bouncing is dominated by the free surface deformation since the bubble has already been highly deformed before collision. We conclude that bouncing of a bubble on a free surface can be explained clearly by the present model based on a simple mass-spring system.